Problem $5$: The Big $M$ Method and The Two$-$Phase Method

Consider the following problem.

minimize,$Z=3x_1+2x_2+4x_3$

subject $to2x_1+x_2+3x_3=60$

$,3x_1+3x_2+5x_{3}120$

$,x_1,x_2,x_{3}0$

Using the Big $M$ method, work through the simplex method step $by$ step $to$ solve the

problem. Identify the optimal solution obtained.

Using the two$-$phase method, work through the simplex method step $by$ step $to$ solve

the problem. Identify the optimal solution obtained.